A vehicle transmission transmits input torque from a prime mover such as an engine or an electric machine to a set of drive wheels through a range of output speeds. In a typical automatic transmission, a hydrodynamic torque converter or an input clutch couples an engine output shaft to a transmission input member. Such a transmission may include various planetary gear sets and hydraulically-actuated clutches, with the various nodes of the planetary gear sets interconnected to each other via the application of different combinations of the clutches. In contrast, a dual-clutch transmission (DCT) has two input clutches for selecting the respective oddly-numbered and evenly-numbered gear sets. In both the multi-speed and the DCT design, a transmission control module executes clutch shift logic to control the necessary clutch sequencing for achieving a requested shift between the different gear sets.